Question: Consider a material test particle that is in a stable circular orbit of coordinate radius r in Schwarzschild spacetime. Suppose we give this particle an

Consider a material test particle that is in a stable circular orbit of coordinate radius r in Schwarzschild spacetime. Suppose we give this particle an infinitesimal outward radial displacement. Calculate the frequency of radial oscillations of this particle according to a clock at infinity. (Astrophysicists call this the radial epicyclic frequency.) Use this to calculate the periapsis precession angle for an orbit with near zero eccentricity (apoapsis radius close to periapsis radius). Check that your formula gives the correct answer for weakly relativistic periapsis precession at large radius

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